All Questions
Tagged with electric-fields vector-fields
159
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Method of image charges for ungrounded conductive sphere seems to have charge of $q$ and not $(r/a) q$?
Using the 2d scenario for simplification
Vector field of a point charge $q=1$ at (-4.1,0):
$$\vec F_1\left( {x,y} \right) = \left(\frac{x+4.1} {{\sqrt{(x+4.1)^2 + (y-0)^2}}^2}\right) \vec e_x + \left(\...
- 155
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69
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$\int \vec{E} \cdot \vec{dA} = (E)(A)$?
I've seen this kind of simplification done very frequently in Gauss's law problems, assuming E is only radial and follows some "simple" geometry:
$$\oint\vec{E}\cdot\vec{dA}=\frac{Q_{enc}}{\...
- 187
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3
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131
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The Curvature of Electric Field Lines
I have been practicing many questions regarding electrical field lines. However, I can't seem to understand when electrical field lines remain straight and when they start to curve. Does it depend on ...
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2
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415
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Accurate drawings of field lines in three situations
I am looking for accurate drawings of the electric and magnetic field lines in three situations:
The electric field lines formed between a positive point charge and negative point charge. (i.e. the ...
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66
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Deriving divergence in cylindrical coordinates, using covariant derivatives
Covariant derivatives are normally used to write equations covariantly in curved spaces. But in an exercise, I need to use covariant derivatives to derive Gauss' law: $\nabla \cdot \vec{E} = 4\pi\rho$ ...
- 145
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1
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132
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In an electrostatic field with zero divergence everywhere, where is the charge located?
Purcell in section 2.17 discusses the electric field $E = <Ky, Kx, 0>$, which has field lines in the shape of a hyperbola, $\phi = -Kxy$, zero curl, and zero divergence. Purcell states that ...
- 309
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86
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What are some ways to derive $\left( \boldsymbol{E}\cdot \boldsymbol{E} \right) \nabla =\frac{1}{2}\nabla \boldsymbol{E}^2$?
For each of the two reference books the constant equations are as follows:
$$
\boldsymbol{E}\times \left( \nabla \times \boldsymbol{E} \right) =-\left( \boldsymbol{E}\cdot \nabla \right) \boldsymbol{E}...
- 105
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156
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Proof for why flux is proportional to number of field lines
What is the proof for this (assuming that we draw infinite field lines).
I understand why flux through some area is proportional to the number of field lines through that area only in the case of an ...
- 81
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2
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171
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Drawing Electric field lines
Suppose there is a medium filled by a charge with the volume density $\rho = \frac{\alpha}{r}$ where $\alpha$ is a positive constant and r is the distance from origin.
Now here if we calculate ...
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1
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66
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Can such a field line exist between two positive charges? [duplicate]
I am aware of the usual diagram of field lines between two positive charges.
My question is that is such a field line wrong, if so why?
- 252
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Curl of the $E$ field of a moving charge
Figure 5.15 from Purcell: "Electricity & Magnetism" (3rd edition) shows the electric field of a uniformly moving charge.
It reads:
The field in Fig. 5.15 is a field that no stationary ...
- 148
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1
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216
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Helmholtz theorem: “There is no function that has zero divergence and zero curl everywhere and goes to zero at infinity”. How do I know this?
I am trying to proof Helmholtz’s theorem and I am currently using David J. Griffith’s book on electrodynamics to do this. Within the book’s Appendix B, (I have not finished the book, and am on the ...
- 39
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1
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76
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Is there a generalization of Gauss's Law for enclosed dipoles, quadrupoles, etc
Given the electrostatic field $\mathbf E$, its integral over a closed surface $\mathcal A$ is the total charge enclosed by it: $$\epsilon_0\oint_{\mathcal A} \mathbf E \cdot d \mathbf A = Q_{\mathcal ...
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4
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64
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Question regarding infinite field lines
In the context of electric field lines, the following is an excerpt from NCERT's Physics Part 1: Textbook for Class XII
Another person may draw more lines. But the number of lines is not
important. ...
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3
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229
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What do electric field lines tell us?
Does it indicate the direction of motion of the photons in electrostatic fields (I mean is the direction of the electric line of force the same as the direction of motion of the photons at that point) ...
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